I can guess what it means, but I would like to have a sentence beginning with What paraphrased fully.

It was 36 years ago. The culture: What 15-year-old girl would tell her parents she had been at a party where kids had been drinking, much less that a boy had attacked her?

The idea is: Could you find a 15-year-old girl who would tell her parents that she had been at a party where kids had been drinking? And even less chance that she would tell them that a boy had attacked her?

In other words, it would have been hard to find such a 15-year-old girl who would do that 36 years ago.

You probably got closer than I did I would say "What possibility would there be that a 15-year-old girl would tell her parents she had been at a party where kids had been drinking, much less that a boy had attacked her?"